By <em>analytical</em> methods and <em>algebraic</em> handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
<h3>How to determine the percentage increase rate </h3>
In this case we have a <em>linear</em> variable x, whose increase is described by the following expression:
y = x · (1 + r/100) (1)
Where r is the <em>increase</em> rate.
If we square (1), then we find that:
y² = x² · (1 + r/100)² = (1 + r'/100) (2)
Where r' is the <em>equivalent increase</em> rate.
(1 + r/50 + r²/10000) = (1 + r'/100)
r'/100 = r/50 + r²/10000
r' = r/2 + r²/100
If we know that r = 25, then the equivalent increase rate is:
r' = 25/2 + 25²/100
r' = 18.75
By <em>analytical</em> methods and <em>algebraic</em> handling and on the basis that x is increased by 25 %, we conclude that the variable x² is increased by 18.75 %.
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